不同差分格式在同位网格系统中的计算效果比较

Effects of Various Difference Schemes on Collocated Grid Systems

针对流体流动数值计算的有限差分法 ,系统地研究了离散对流项的 6种差分格式 :CDS、FUDS、HDS、PLDS、SUDS和QUICK·比较计算采用同位网格系统·采用两个有分析解或基准解的算例 ,就不同格式对数值求解N S方程的精度、稳定性和收敛特性的影响进行了分析比较·计算结果表明 ,当扩散项占主导地位时 ,所有格式在同位网格中几乎具有相同的计算精度·随着对流项的增加直到占主导地位 ,FUDS、HDS和PLDS的在同位网格中具有相同的精度 ,而SUDS和QUICK的精度比前三种高 ,CDS次之·对于相同的速度、压力松弛因子和收敛准则 ,各种格式在同位网格中的收敛速度相差甚微·

Six difference schemes including CDS, FUDS, HDS, PLDS, SUDS and QUICK for convection terms in numerical fluid flow based on the finite difference method were systematically investigated. The computations were performed on the collocated grid system. Effects of accuracy, stability, and convergence characteristics of the schemes on the solutions of the Navier Stokes equations were analyzed respectively. The results indicate that, all schemes have the same effects on computational efforts when the diffusion term is predominant on collocated grid. With the increase of convection, or the convection to be dominant, the FUDS, HDS and PLDS have almost the same accuracy on the two grids, while the SUDS and QUICK have higher accuracy than the formers and the CDS is in the middle. For the same under relaxation parameters of velocity and pressure and the same convergence criterion, the convergence rates of each scheme are nearly equal.